Hello can someone please help with this question?

Consider the sequence an+1 =sqrt(2 + an)

Show that for all n in natural numbers.

n+1 - a= (an=-an-1)/(sqrt(2+an+sqrt(2+an-1))

I really don't understand what to do?

I think what you mean is this:

a_{n+1} - a_n = \frac {a_n - a_{n-1}}{\sqrt{2+a_n}+\sqrt{2+a_{n-1}}}

It's simply a matter of using the definition, and incrementing backwards from a_{n+1} to a_n. To get you started, from the definition of a_{n+1} you get:

a_n = \sqrt{2 + a_{n-1}}

so:

a_{n+1}-a_n = \sqrt{2 + a_n} - \sqrt{2 + a_{n-1}}

Can you take it from here?